Number.Peano

Lazy Peano numbers represent natural numbers inclusive infinity. Since they are lazily evaluated, they are optimally for use as number type of genericLength et.al.

Documentation

data T

Constructors

Zero

Succ T

Instances

Bounded T

Enum T

Eq T

Integral T

Num T

Ord T

Read T

Real T

Show T

Ix T

C T

C T

C T

C T

C T

C T

C T

C T

C T

C T

C T

C T

C T

infinity :: T

err :: String -> String -> a

add :: T -> T -> T

sub :: T -> T -> T

subNeg :: T -> T -> (Bool, T)

mul :: T -> T -> T

fromPosEnum :: (C a, Enum a) => a -> T

toPosEnum :: (C a, Enum a) => T -> a

ifLazy :: Bool -> T -> T -> T

If all values are completely defined, then it holds

 if b then x else y == ifLazy b x y

However if b is undefined, then it is at least known that the result is larger than min x y.

argMinFull :: (T, a) -> (T, a) -> (T, a)

cf. To how to find the shortest list in a list of lists efficiently, this means, also in the presence of infinite lists. http://www.haskell.org/pipermail/haskell-cafe/2006-October/018753.html

argMin :: (T, a) -> (T, a) -> a

On equality the first operand is returned.

argMinimum :: [(T, a)] -> a

argMaxFull :: (T, a) -> (T, a) -> (T, a)

argMax :: (T, a) -> (T, a) -> a

On equality the first operand is returned.

argMaximum :: [(T, a)] -> a

isAscendingFiniteList :: [T] -> Bool

x0 <= x1 && x1 <= x2 ... for possibly infinite numbers in finite lists.

isAscendingFiniteNumbers :: [T] -> Bool

toListMaybe :: a -> T -> [Maybe a]

glue :: T -> T -> (T, (Bool, T))

In glue x y == (z,(b,r)) z represents min x y, r represents max x y - min x y, and x<=y == b.

Cf. Numeric.NonNegative.Chunky

isAscending :: [T] -> Bool

data Valuable a

Constructors

Valuable

Fields

costs :: T

value :: a

Instances

Eq a => Eq (Valuable a)

Ord a => Ord (Valuable a)

Show a => Show (Valuable a)

increaseCosts :: T -> Valuable a -> Valuable a

(&&~) :: Valuable Bool -> Valuable Bool -> Valuable Bool

Compute '(&&)' with minimal costs.

andW :: [Valuable Bool] -> Valuable Bool

leW :: T -> T -> Valuable Bool

isAscendingW :: [T] -> Valuable Bool

notImplemented :: String -> a